Bipartite charge fluctuations in one-dimensional ${\mathbb{Z}}_2$ superconductors and insulators

Abstract

Bipartite charge fluctuations (BCF) have been introduced to provide an experimental indication of many-body entanglement. They have proved themselves to be a very efficient and useful tool to characterize quantum phase transitions in a variety of quantum models conserving the total number of particles (or magnetization for spin systems). In this Letter, we study the BCF in generic one-dimensional ${\mathbb{Z}}_2$ (topological) models including the Kitaev superconducting wire model, the Ising chain or various topological insulators such as the SSH model. The considered charge (either the fermionic number or the relative density) is no longer conserved, leading to macroscopic fluctuations of the number of particles. We demonstrate that at phase transitions characterized by a linear dispersion, the BCF probe the change in a winding number that allows one to pinpoint the transition and corresponds to the topological invariant for standard models. Additionally, we prove that a sub-dominant logarithmic contribution is still present at the exact critical point. Its quantized coefficient is universal and characterizes the critical model. Results are extended to the Rashba topological nanowires and to the XYZ model.

6 pages + Supp Mat (6 pages), to be submitted, all comments are welcomed

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Cited by in corpus (8)

• Full Counting Statistics in the Transverse Field Ising Chain
• Majorana Spin Liquids, Topology and Superconductivity in Ladders
• Formation probabilities and statistics of observables as defect problems in the free fermions and the quantum spin chains
• From Topological Superconductivity to Quantum Hall States in Coupled Wires
• Bipartite Fluctuations and Topology of Dirac and Weyl Systems
• Cusps near Topological Phase Transitions: Signatures of Majorana fermions and interactions with fluctuations
• Valence bond fluctuations in the Kitaev spin model
• Dynamically Induced Topology and Quantum Monodromies in a Proximity Quenched Gapless Wire